In this paper, we investigate the impact of maturation delay on the positive equilibrium solutions in a stage-structured predator prey system. By analyzing the characteristic equation we derive the conditions for the ...In this paper, we investigate the impact of maturation delay on the positive equilibrium solutions in a stage-structured predator prey system. By analyzing the characteristic equation we derive the conditions for the emergence of Hopf bifurcation. By applying the normal form and the center manifold argument, the direction as well as the sta- bility of periodic solutions bifurcating from Hopf bifurcation is explored. Results show that maturation delay can change the nature of the positive equilibrium solutions, and the loss of equilibrium stability occurs as a consequence of Hopf bifurcation. When Hopf bifurcation takes place, periodic solution arises and is further demonstrated to be asymptotically stable. In addition, the periodic solutions appear only for intermediate maturation delay, that is, there exists a delay window, outside of which the positive equilibrium is locally stable. Furthermore, numerical analysis shows that Hopf bifur- cation is favored by a superior competition for adult predators to juveniles, a smaller mortality on juvenile and/or adult predators, and a higher resource carrying capacity. Interestingly, increasing food carrying capacity can lead to the emergence of irregular chaotic dynamics and regular limit cycles.展开更多
文摘In this paper, we investigate the impact of maturation delay on the positive equilibrium solutions in a stage-structured predator prey system. By analyzing the characteristic equation we derive the conditions for the emergence of Hopf bifurcation. By applying the normal form and the center manifold argument, the direction as well as the sta- bility of periodic solutions bifurcating from Hopf bifurcation is explored. Results show that maturation delay can change the nature of the positive equilibrium solutions, and the loss of equilibrium stability occurs as a consequence of Hopf bifurcation. When Hopf bifurcation takes place, periodic solution arises and is further demonstrated to be asymptotically stable. In addition, the periodic solutions appear only for intermediate maturation delay, that is, there exists a delay window, outside of which the positive equilibrium is locally stable. Furthermore, numerical analysis shows that Hopf bifur- cation is favored by a superior competition for adult predators to juveniles, a smaller mortality on juvenile and/or adult predators, and a higher resource carrying capacity. Interestingly, increasing food carrying capacity can lead to the emergence of irregular chaotic dynamics and regular limit cycles.
